Effective Reasoning/Informal and Formal Reasoning

Formal reasoning is concerned only with the forms of arguments. Certain forms of arguments have been identified which are valid. In other words, if the original statements (or premises) in those arguments are true, then the conclusions must necessarily be true also. Therefore, the form:

All marbles are red. All red things are bright. Therefore, all marbles are bright.

is a valid form.

The truth of the first two statements is not of interest. But, assuming that they are true, the last statement must necessarily be true.

Formal reasoning is deductive in nature. In other words, as said above, the conclusion of a valid formal argument follows necessarily from the premises. Notice that deductive reasoning produces no new information. It simply rearranges what is already known into a new statement of the same information.

Notice also that deductive or formal reasoning does not require any reference to external reality. It can be completely divorced from external reality. Therefore:

All unicorns are white. All white things are virtuous. Therefore, all unicorns are virtuous.

is a prefectly good and valid deductive argument.

Formal reasoning is addressed in other Wikibooks - Formal Logic, and Systems of Logic.

Informal reasoning includes formal reasoning but it also is concerned with all the other elements of reasoning. It addresses the probability of truth of premisses and conclusions. Informal reasoning is common, every-day reasoning.